The Construction On Exact Solutions To Several Classes Of Partial Differential Equations

In solitary theory, the construction on exact solutions of nonlinear evolution equations is paid much attention. Riccati equation method and the triangular function method are direct and effective methods. This paper contains two main parts, that is, how to construct the exact solutions of nonlinear continuous partial differential equations and how to seek the exact solutions of nonlinear difference-differential equations.In Chapter two, based on the auxiliary equation method, the solutions of Riccati equation are given, and then the Riccati equation method is applied to construct new exact solutions of nonlinear continuous partial differential equations. To illustrate the method, Burgers equation and Klein-Gordon equation are chosen as examples and a number exact solutions of the equations are obtained with the help of symbolic computation system Maple, which include hyperbolic function solutions, triangular function solutions and rational function solutions. The method is of significance to seek exact solutions of other nonlinear equations. Chapter three will present some special solutions of Riccati equation, then Riccati equation is applied to solve nonlinear difference-differential equations, and hyperbolic function solutions and triangular function solutions to nonlinear discrete mKdV lattice equation and (2+1)-dimensional Toda lattice equation are obtained with the help of symbolic computation system Maple. Besides that, based on trial function method and tanh-function method, a kind of triangular function expansion is introduced and applied to construct new triangular function solutions of nonlinear discrete mKdV lattice equation and nonlinear discrete Hybrid lattice with the aid of symbolic computation system Maple.